[icebraining]

Given a metallic backing, and a regular fridge-magnet-like magnet, is there some way to trade some of the magnetic force the magnet is exerting on the backing for electrical power?

You need movement to generate electricity, otherwise it'd be a perpetual machine.

An alternative would be to have a "surface of light", ie, a source of light all along one of the walls of the map and passing right over it (not actually illuminating the map); then any object sitting on the map would be illuminated.